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Theoretical Research

I am primarily interested in auditory biophysics, chiefly in the context of how sound is transduced by the ear into neural impulses going to the brain. Remarkably, somehow in the process of being a very sensitive detector, the (healthy) ear generates and subsequently emits sounds that can be detected non-invasively using a sensitive microphone. These sounds, known as otoacoustic emissions (OAEs), reveal many aspects of the inner workings of the ear and also have many translational applications (e.g., clinical audiology). Our lab combines both experimental and theoretical/modeling approaches across a broad comparative framework so to help us better understand OAEs and thereby the key biophysical processes at work that allow us to hear the world around us.

In recent years, the availability of intense positron beams allowed for an increase in the number of ionization experiments. The first experiments, which studied noble gases, were followed by measurements of the ionization cross sections for other atoms and molecules and for triple differential cross section measurements. Our work uses various theoretical models to reproduce the existing experimental cross sections. For the calculation of the total ionization cross sections of atoms and molecules, we have explored the use of distorted-wave models, containing a realistic description of the final state of the system and including distortion and polarization effects. Recently, we expanded our work to the study of the electron-capture-in-the-continuum (ECC) phenomenon in positron impact ionization of helium and molecular hydrogen. We employed a 3C theoretical model in representing the final state of the ionization system, which allowed us to obtain good agreement with the existing "triple differential cross section" experiments.

I am an active developer of advanced numerical modeling and data assimilation systems for studying weather and climate. I utilize state-of-the-art numerical models and ensemble-based data assimilation techniques to improve weather forecasts, regional climate predictions, and air-quality forecasts. Particularly, I am interested in mesoscale dynamics and severe weather.

My current research is concerned with the development and application of variational (i.e non-perturbative) methods in quantum field theory. I am particularly interested in using the variational method to derive (and solve) relativistic few-body wave equations from the underlying quantum field theory. I investigate model quantum field theories, such as the Yukawa model, as well as QED and various sectors of the standard model. In addition, I am interested in positron interactions with simple molecules and atoms, particularly ionization and annihilation, as well as bounded variational methods in quantum scattering theory.

Using various methods of computational chemistry in combination with global optimization and simulation methods, I study atomic clusters that range in size from 3 atoms to a few hundred atoms. The geometric structure and properties of small clusters are very different from those of the corresponding bulk materials. For example, silver clusters are not fragments of the fcc crystal, and clusters of rhodium are magnetic. Our theoretical predictions of vibrational spectra and electron detachment energies are compared to experiment for structure elucidation. We try to understand the factors controlling stability, so that we might predict cluster sizes and compositions that are particularly stable. We also model surfaces and noncrystalline materials with clusters having a hundred or more atoms using more approximate theoretical models, such as empirical potentials and model hamiltonians. I am also interested in molecular ions and transition metal complexes.

When matter spirals into a supermassive black hole at the centre of a galaxy, a kind of friction can heat the matter up until it shines brightly enough to be seen all the way across the universe. We call such objects quasars. I am interested in understanding more clearly the dynamics of gas spiralling around black holes in quasars. That knowledge will improve our ability to infer the physical properties of quasars and their black holes (such as mass and spin) from the details of the light they produce. I am particularly interested in outflows of gas from quasars. Much of the mass spiralling around in a quasar ends up in the black hole, but some of it is flung outwards and is sometimes visible in the spectrum of the quasar. Establishing the connections between those absorption lines and the emission lines seen in most quasars will help us understand how quasars work and how galaxies form. I am also interested in gravitational lensing, which can take a small, faint galaxy and stretch it out into a long, luminous arc. My research is both experimental and theoretical. I do much of my experimental work using online databases from large astronomical surveys, supplementing data as necessary with modern instruments on large telescopes.

My professional research goals centre around the investigation and solution of mathematical and computational problems of scientific and engineering relevance. During the last few years, I have worked on a variety of highly applied and very challenging problems in electromagnetics, hydrodynamics, and combinations of both. For example, I have researched wire antenna problems, numerical methods for optical gratings, enhanced radar backscatter from the ocean surface, hydrodynamic stability problems, blood flow in compressed vessels, and the hydrodynamics of expanding universes. Certainly, computational science lies at the core of my research interests.

The main goal of computational electromagnetics, for example, is the design and implementation of numerical methods that can be used to efficiently simulate electromagnetic wave interactions with complex material structures. This field has shown an impressive growth in recent years, as improved numerical algorithms enable accurate simulation of the ever more complex phenomena arising in an ever growing number of applications. The numerical methods used in this area draw from the classical approaches, such as the method of moments and finite-element based algorithms into the efficient high-order/accelerated algorithms that have arisen over the last two decades. Applications are found in communications (transmission through optical fiber or wireless communication), remote sensing and surveillance (radar and sonar systems), geophysical prospecting, materials science, and biomedical imaging (optical coherence tomography), to name but a few.

Significant challenges arise in the design of reliable numerical algorithms for engineering and industrial applications such as those mentioned above. These challenges are largely due to the necessity of numerical methods to resolve wave oscillations and interactions of these with geometrically and/or compositionally complex structures, which lead to very high (often prohibitive) computational costs for many problems of interest. The focus of my work has been and will continue to be the development and implementation of efficient, fast and accurate numerical algorithms to enable treatment of challenging engineering and scientific applications.

I employ lasers to make high-precision measurements of atomic properties to test the predictions of Quantum Electrodynamics and the Standard Model of particle physics. Currently, I am studying atomic hydrogen to make a new measurement of the radius of the proton to try to understand the deviant value recently obtained from muonic hydrogen. If the discrepancy is real, it may herald the discovery of a new boson or even gravity in higher dimensions. Also, I am part of a collaboration whose goal is to hold antihydrogen atoms (antimatter versions of the element hydrogen) in a magnetic trap and use them to conduct precise spectroscopic tests of the symmetries and physics of antimatter. Additionally, I am involved in measuring the energies and orbits of helium atoms to provide the most accurate measurement of the "fine structure constant,” the fundamental constant of nature that determines the strength of the electric and magnetic forces between charged objects. The fine structure constant is not only relevant to magnets and electricity, but to how atoms, chemicals, and solid objects are held together.

I study interactions of atoms and simple molecules in collisions with ions or in exposure to strong laser fields by theoretical and computational methods. My particular interests are in the areas of multiple ionization and capture of electrons in collisions of highly charged ions. Also, I am interested in quantum optics, especially in measurements of the radius of the proton and the line shape problem for high-precision spectroscopy, as well as the problem of electron-positron pair creation in ultra-strong fields. My emphasis is on developing new computational methods and testing time-dependent density functional theory.

The goal of my research is to understand the fundamental laws of nature through their impact on cosmology. I am primarily a theorist, dabbling in cosmology, field theory, string theory, and gravitation. I am actively engaged in research on cosmic inflation, eternal inflation, topological defects, and models of dark energy. I also design data analysis algorithms to confront fundamental theory with observations of the Cosmic Microwave Background (CMB) radiation. Here is a sampling of the questions that drive my research: How big is the universe? What might lie beyond our observable universe, and how could we confirm or disprove various proposals? What role do the extra dimensions predicted by string theory play in cosmology? What is the fundamental nature of space-time singularities? Are there new ways of looking at cosmological datasets that could be useful when confronting theories with data? Can computer simulations of the very early universe shed light on its possible initial conditions and evolution?

My research is concerned with the question of how atomic and molecular few-body systems respond to perturbations exerted on them by impinging particles and external fields. Quantum dynamics induced by collisions or laser fields have implications for a variety of topics and applications ranging from plasma diagnostics to radiation biology. What is more, they constitute a problem of fundamental importance: How do the building blocks of matter interact and evolve in space and time? The better this question is answered, the more is learned about a further issue that receives considerable attention: Can few-body quantum dynamics be manipulated purposefully and controlled actively?

I have participated in a number of projects and activities to elucidate these topics by theoretical analysis and computations. Methods based on density functional theory deal with the many-electron problem, and both nonperturbative and perturbative quantum methods describe the dynamics of the systems. Currently, we are working on a method to describe ionization and fragmentation of multi-center molecules. First applications are concerned with ion-induced fragmentation of water, which is a relevant process in the radiation damage of biological tissue. In the long run we hope to study even more complex systems, thereby exploring the transition from correlated to collective dynamics. Our central goal is to contribute to a microscopic understanding of time-resolved quantum dynamics, and to investigate applicability and limitations of density functional theory by practical calculations.

I aim to understand strongly coupled quantum field theories, quantum chromodynamics (QCD) in particular. QCD is the theory of the nuclear and sub-nuclear strong force, the force that binds protons and neutrons to form nuclei and at a deeper level, the force that binds quarks to form neutrons and protons. Although the theory can be stated very compactly and elegantly, its solution has eluded physicists for decades. This is perhaps not surprising as QCD can be thought of as a theory of 104 complex-valued quantum variables at each point in space. One of the most promising approaches for studying QCD is Monte-Carlo simulation of the field theory on a space-time lattice. I use this technique to study nuclear forces, colour-flux-tube breaking and other problems.

Inside the protons and neutrons of every atom's nucleus, there are quarks. The strong force that is responsible for the perpetual confinement of quarks is described by Quantum Chromodynamics (QCD). My recent research has combined theoretical methods with supercomputer simulations to explore this quantum theory of quarks via lattice QCD computations, chiral perturbation theory, and heavy quark symmetry. My work also extends to theories beyond the Standard Model of particle physics.

I am interested in the consequences of the Standard Model of particle physics for few-body nuclear systems and low-energy particle physics and dynamics. My recent research has focussed on Quantum Chromodynamics (QCD), the theory of the strong interactions, using the techniques of chiral perturbation theory and various versions of QCD sum rules to study weak, strong, and electromagnetic observables.

My work is in theoretical atomic physics. I am particularly interested in electron and positron scattering, both elastic and inelastic, and I endeavour to calculate cross sections for a wide range of targets. Such cross sections are essential to understanding how matter behaves in a wide range of environments, be they natural (e.g., the Earth’s atmosphere, or astrophysical plasmas) or constructs of humans (e.g., fission or fusion reactors).

I carry out theoretical research on the scattering of electrons and positrons from atoms and simple molecules. I am particularly interested in scattering from heavy atoms, and use the relativistic Dirac equations as the basis for computation of scattering parameters. Collaborating with graduate students and international co-workers, we perform large scale numerical computations of these processes and develop theoretical and numerical methods to carry them out. For example, we have developed the very successful Relativistic Distorted-Wave Method for evaluating the scattering cross sections as well as the spin polarization parameters for the scattered electrons and the Stokes parameters for the light emitted from atoms excited during the scattering interactions. I am also involved in projects which make use of the atomic data we generate. Much of our work is of use in plasma physics, particularly in the modeling of low pressure plasmas. One example is a large-scale Monte Carlo simulation of gas-filled X-ray detectors. I maintain close contact with various experimental groups and often publish joint papers with these groups where theory and experiment can be directly compared.

Dark matter makes up around 85% of the matter in the Universe and yet we have no explanation for it in the Standard Model of particle physics. As a particle theorist, my research focuses on proposing new ideas and new tests for dark matter in order to illuminate what this mysterious stuff actually is. Recently, I have become interested in using astronomical observations of galaxies and clusters to determine whether dark matter particles interact with each other through forces other than gravity. It is remarkable that the largest structures in the Universe, millions of light years in size, can be a laboratory to study the microscopic properties of dark matter particles. I also explore the idea that dark matter is made up of strongly-interacting constituents, much like protons and neutrons. Theories of this nature cannot be worked out using paper-and-pencil and I collaborate with lattice theorists to simulate dark matter's properties using supercomputers.

My research interests include computational solid mechanics, dynamics of mechanical systems, and numerical methods and their applications in the aerospace and defence industries. I am particularly interested in space tethers, such as the dynamics and control of tethered spacecraft systems and the application of electrodynamic tether control to the removal of space debris. Other applications include aerial refuelling systems, aerial cable-towed instruments, and underwater cable-towed systems. Additionally I am engaged in developing autonomous space robotics for on-orbit servicing. In support of many of these endeavours, I also study multi-functional composite materials and additive manufacturing in space.

I study the way the brain represents information about the outside world, and the way in which those representations are learned. My immediate goal is to build on my expertise in machine learning and sensory neuroscience to create a camera to brain translator that could restore sight to the blind, and could be used in computer vision systems. In parallel, I will develop new data science methods that will infer the brain’s learning rules from in vivo neural data, and use those methods to determine how behavioural context affects synaptic plasticity in the visual cortex. Next, I will use the brain’s learning rules to make next-generation machine learning algorithms that will be more flexible and efficient than the current state of the art. Finally, I will reveal how the interaction between different retinal ganglion cell types supports the communication of visual information from the eyes to the brain. That work may have strong implications for the development of next-generation retinal prosthetics.